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If the set $\{a,b,c,d,e,f,g\}$ is is partitioned into these three partitions:

$\{a, c, e, g\}$

$\{b, d\}$


and an equivalence relation is produced by these partitions, is $\{a,c,e,g\}$ an equivalence class?

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That's not a partition: b is in two sets, and c is in none. – Chris Eagle Dec 7 '11 at 0:37
The relation you have defined ("$a~b$ iff $a$ and $b$ are both in the same set) not transitive: $a~b$ and $b~d$ but $a$ is not related to $d$. – Neal Dec 7 '11 at 0:41
Crap. I meant for the first one to say {a, c, e, g} instead of {a, b, e, g}. Fixed it now; thanks for pointing it out. – Josh1billion Dec 7 '11 at 0:53
up vote 2 down vote accepted

As updated, yes. Wikipedia has more

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Perfect, just what I needed to know. Thanks. – Josh1billion Dec 7 '11 at 0:59

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